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A336377
Primes p(n) such that gcd(n, prime(n)+prime(n+2)) > 1.
4
3, 7, 13, 19, 23, 29, 37, 43, 53, 61, 71, 73, 79, 89, 97, 101, 107, 113, 131, 137, 139, 151, 163, 173, 181, 193, 197, 199, 223, 229, 233, 239, 251, 263, 269, 271, 281, 293, 311, 317, 337, 349, 359, 373, 379, 383, 397, 409, 421, 433, 443, 457, 463, 479, 491
OFFSET
1,1
COMMENTS
This sequence and A336376 partition the set of primes.
EXAMPLE
In the following table, p(n) = A000040(n) = prime(n).
n p(n) p(n)+p(n+2) gcd
1 2 7 1
2 3 10 2
3 5 16 1
4 7 20 4
5 11 28 1
6 13 32 2
1 and 3 are in A336374; 2 and 4 are in A336375; 2 and 5 are in A336376; 3 and 7 are in A336377.
MATHEMATICA
p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &] (* A336374 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &] (* A336375 *)
Prime[u] (* A336376 *)
Prime[v] (* A336377 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 06 2020
STATUS
approved